5th Grade Math
Notes & Resources
Problem Solving Resources
Quarter 1 Table of Contents
Quarter 2 Table of Contents
Quarter 3 Table of Contents
Quarter 4 Table of Contents
Data & Graphing
🎯Learning Targets:
Classifying Data
Data can be classified in two different ways.
Categorical Data
Numerical Data
Data that Changes Over Time
Data that include characteristics.
Examples: names, locations, food, personal preferences.
Also called qualitative data.
Data that can be counted or measured.
Examples: number of baseball cards, inches of snow on one day, number of siblings
Also called quantitative data.
Special kind of data that shows data collected over time.
Examples:rainfall totals for a w
eek, student’s height from ages 1 to 10.
Example:
Categorical Data | Numerical Data | Data that Changes Over Time |
| | |
Students tell how many years they’ve attended school.
Students name the types of pets they have.
A class collect data on which place they’d like to visit for a vacation.
Student records number of pages they read each day.
A business collects data on their profits each year to see if they’re increasing or decreasing.
Number of students enrolled in each class.
Coordinate Planes
Solving Problems involving Coordinate Planes
Graphing Patterns on a Coordinate Plane
rules that can be applied to get future numbers in a sequence
a grid showing the ‘x’ and ‘y’ coordinates of ordered pairs
numbers appearing in the same location in different sets
a set of two numbers that define a point on a coordinate plane
Pattern
Key Vocabulary
Corresponding Terms
Ordered Pair
Coordinate Plane
Video Game
When we write our ordered pairs, we are putting CORRESPONDING TERMS together.
The rule for corresponding terms can be written in several ways:
X * 6 = Y 6X =Y
6 times X = Y
Or: Y divided by 6 = X
🎯Learning Targets:
Using A Line Graph to Determine a Pattern
How can we use a line graph to determine a pattern?
x | y | (x,y) |
1 | 3 | ( 1, 3 ) |
2 | 4 | ( 2, 4 ) |
3 | 5 | ( 3, 5 ) |
4 | 6 | ( 4, 6 ) |
5 | 7 | ( 5, 7 ) |
6 | 8 | ( 6, 8 ) |
7 | 9 | ( 7, 9 ) |
First, we must list the ordered pairs.
Noticing Patterns
x | y | (x,y) |
1 | 3 | ( 1, 3 ) |
2 | 4 | ( 2, 4 ) |
3 | 5 | ( 3, 5 ) |
4 | 6 | ( 4, 6 ) |
5 | 7 | ( 5, 7 ) |
6 | 8 | ( 6, 8 ) |
7 | 9 | ( 7, 9 ) |
Start with 1 and add 1
Start with 3 and add 1
X + 2 = Y and Y - 2 = X
Multiplying with Zero
Area Model of Multiplication
Standard Algorithm of Multiplication
Standard Algorithm-
Turtle Head Method
Connecting the Area Model Method to the Standard Algorithm
Volume with Unit Cubes
MATHEMATICAL VOCABULARY
Rectangular Prism | A solid three-dimensional figure in which all 6 faces are rectangles. | |
Dimension | A measurement of length in one direction (ex. depth width, height) | |
Volume | The amount of space a solid figure takes up. | |
Cubic Units | the units used to measure volume | |
Calculating Volume
How to find a missing dimension
Volume of Irregular Figures:
Additive or Composite Volume
Solving Problems with Volume
Area Model of Division
Partial Product Method
Dividend
Definition: The number that is divided in a division problem.
Examples:
Divisor
Definition: The number that divides the dividend in a division problem.
Examples:
Quotient
Definition: The result of the division in a division problem.
Examples:
Remainder
Definition: The number left over after dividing two numbers that are not evenly divisible.
Examples:
Standard Algorithm of Division
2 Digit Divisor Division
Expressions, Equations & Variables
Expression | A variable or combination of variables, numbers, and symbols that represents a mathematical relationship. | a + 3 x b |
Equation | A statement that two mathematical expressions are equal. | 4 x 6 = 8 x 3 |
Variable | A symbol used to represent an unknown value. The “b” and “$” are variables | 4 x b 3 + $ |
Order of Operations
Decimal Place Value
Decimals- Standard, ExpaNded & Word Form
Decimals On A Number Line
Comparing Decimals
Understanding Place Value
Increases & Decreases by Powers of Ten
Adding & Subtracting Decimals With Models
Adding & Subtracting Decimals
Multiplication as Scaling- Fractions
Multiplying Fractions by Whole Numbers
Multiplying Fractions by Fractions
Multiplying Fractions with Cross-Cancellation
Multiplying Mixed Numbers
Fractions As Division
Dividing
Whole Numbers
By Unit Fractions
Dividing Unit Fractions By
Whole Numbers
Add & Subtract Fractions
MathAntics - Start at 6:14
Multiply Decimals
With Models
Multiply Decimals
RIGHT, count the total
4608.
Divide Decimals By Whole Numbers
Divide Whole Numbers By Decimals
Divide Decimals By Decimals
Properties of Quadrilaterals
What conclusions can we draw from the graphic?
Quadrilaterals
Have 4 sides and 4 angles
Parallelogram
Has opposite sides that
are equal and parallel.
Trapezoid
Has 1 pair of
parallel sides.
Rectangle
Has 4 right angles.
Opposite sides are
equal and parallel.
Rhombus
Has 4 equal sides.
Opposite sides
are parallel.
Square
Has 4 equal sides and
4 right angles.
A square can also be called a rhombus, a rectangle, a parallelogram,
and a quadrilateral.
A rectangle can also be called a parallelogram and a quadrilateral.
A rhombus can also be called a parallelogram and a quadrilateral.
A parallelogram can also be called a quadrilateral.
A trapezoid is a quadrilateral.
What conclusions can we draw from the graphic?
Customary Length
Conversions
Length 1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5,280 ft 1 mi = 1,760 yd 1 yd = 36 in | Conversions: Feet to inches (BLT) multiply by 12 Inches to feet (LBD) divide by 12 Yards to feet (BLT) multiply by 3 Feet to yards (LBD) divide by 3 Miles to feet (BLT) multiply by 5,280 Feet to miles (LBD) divide by 5,280 Miles to yards (BLT) multiply by 1,760 Yards to miles (LBD) divide by 1,760 Yards to inches (BLT) multiply by 36 Inches to yards (LBD) divide by 36 |
Customary Weight
Conversions
Customary Weight 1 pound (lb) = 16 ounces (oz) 1 Ton (T) = 2,000 lbs | Conversions: Pounds to ounces (BLT) multiply by 16 Ounces to pounds (LBD) divide by 16 Tons to lbs (BLT) multiply by 2,000 Lbs to T (LBD) divide by 2,000 |
Customary Capacity
Conversions
Capacity 1 gallon(gal)= 4 quarts (qt) 1 gal = 8 pints (pt) 1 gal =16 cups (c) 1 gal =128 fluid oz 1 qt = 2 pt 1 qt = 4 c 1 qt = 32 fl. oz. 1 pt = 2 c 1 pt = 16 fl oz 1 c = 8 fl oz |
Metric System Conversions